Question: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-x+6y &= 3 \\ 4x-8y &= 4\end{align*}$
Solution: Begin by moving the $x$ -term in the second equation to the right side of the equation. $-8y = -4x+4$ Divide both sides by $-8$ to isolate $y$ $y = {\dfrac{1}{2}x - \dfrac{1}{2}}$ Substitute this expression for $y$ in the first equation. $-x+6({\dfrac{1}{2}x - \dfrac{1}{2}}) = 3$ $-x + 3x - 3 = 3$ Simplify by combining terms, then solve for $x$ $2x - 3 = 3$ $2x = 6$ $x = 3$ Substitute $3$ for $x$ back into the top equation. $- 3+6y = 3$ $-3+6y = 3$ $6y = 6$ $y = 1$ The solution is $\enspace x = 3, \enspace y = 1$.